Mathematics for FinancePYQ Sep 24Question 1483 of 512
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A loan of 16,550\displaystyle 16,550 is to be paid in three equal annual instalments at compound interest. The value of annual instalment, if the rate of interest is 10%\displaystyle 10\% per annum is:

Options

A1,243\displaystyle 1,243
B6,655\displaystyle 6,655
C6,565\displaystyle 6,565
D1,343\displaystyle 1,343
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Correct Answer

✅ Option b — 6,655\displaystyle 6,655

All Options:

  • A1,243\displaystyle 1,243
  • B6,655\displaystyle 6,655
  • C6,565\displaystyle 6,565
  • D1,343\displaystyle 1,343

Detailed Solution & Explanation

The present value of an ordinary annuity (loan amount) is: PV=P×[1−(1+i)−ni]PV = P \times \left[ \frac{1 - (1+i)^{-n}}{i} \right] Given: * Loan amount (PV\displaystyle PV) = 16,550\displaystyle 16,550 * Time (n\displaystyle n) = 3\displaystyle 3 years * Interest rate (i\displaystyle i) = 10%\displaystyle 10\% p.a. = 0.10\displaystyle 0.10 First, calculate the annuity factor: Factor=1−(1.10)−30.10=1−0.75131480.10=2.48685\text{Factor} = \frac{1 - (1.10)^{-3}}{0.10} = \frac{1 - 0.7513148}{0.10} = 2.48685 Now solve for the annual instalment P\displaystyle P: 16,550=P×2.4868516,550 = P \times 2.48685 P=16,5502.48685=6,655P = \frac{16,550}{2.48685} = 6,655 Thus, the annual instalment is 6,655\displaystyle 6,655. Hence, **Option B** is the correct answer.

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